Republic has come to mean a society where there is no hereditary or appointed monarch or emperor (monarchy) as head of state. Republics vary widely in their ideology and composition, though the most common definition of a republic is a state without a monarch.
Originally Republic referred to a system of political rule where citizens, through representative institutions participated in government and exercised political power. Historically, republics contained an aristocratic class with hereditary titles and privileges. Republic derives from the original Latin res publica which means things public, those things that are connected to ruling the public realm. The term republic originated from the writers of the Renaissance such as Machiavelli as a descriptive term for states that were not monarchies.
In its narrower meaning the term Republic distinguishes Canada, Britain, Norway, Sweden, Denmark, the Netherlands, Thailand and other countries formally headed by monarchs, from France, Italy, Germany, the United States and many others where the head of state is a president either directly elected or appointed by an elected group.
In the United States republic refers to representative democracy and republicanism refers to a specific ideology that is based on civic virtue.
Parliamentary republic, Federal republic, Islamic Republic, Arab Republic, and Democratic Republic are some of the phrases used to describe and distinguish the type and nature of the various republics.
A number of states of the classical era that are today by convention called republics includes the states of Ancient Greece such as Athens and Sparta and the Roman Republic.